FLT CREW OF LJ60 LOSE HDG INFO SHORTLY AFTER TKOF FROM LGA. RETURN TO ARPT CAUSES CONFUSION AND EXTRA HANDLING FROM APCH CTLRS.

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I WAS THE FO ON A PART 135 CHARTER FLT OUT OF LGA. AFTER OUR PAX ARRIVED WE WENT TO THE AIRPLANE AND GOT THINGS SETTLED AND READY FOR DEP. AFTER THE CAPT STARTED THE ENGS HE NOTICED AND POINTED OUT TO ME THAT THE STORM-SCOPE WAS NOT WORKING AND HAD AN ERROR MESSAGE. NEITHER ONE OF US THOUGHT ANYTHING OF IT AT THE TIME BECAUSE IT WAS VFR AND WE DIDN'T NEED IT. TFC WAS HVY THAT MORNING AND WE TAXIED FOR ABOUT HALF AN HR AND JUST BEFORE WE RECEIVED OUR TKOF CLRNC ON THE CAPT'S MFD HE GOT A RED HDG FLAG (HD) AND A RED FLT DIRECTOR FLAG (FD) AND HIS HDG WAS NOT ACCURATE AND SOON AFTER HIS SIDE FAILED MY SIDE FAILED WITH THE SAME WARNING FLAGS. AFTER LINING UP ON THE RWY THE SYS WAS RUNNING AGAIN BUT AT THAT POINT WE OPTED TO NOT TAKE OFF AND WE TAXIED CLR OF THE RWY TO TRY AND SOLVE THE PROB. THE CAPT SHUT THE SYS DOWN TO TRY AND REBOOT THE SYS AND WHEN THINGS CAME BACK UP IT ALL SEEMED TO BE OK. THE HDGS WERE A LITTLE ODD BUT WORKING. WE THEN LINED UP ON THE RWY AGAIN AFTER RECEIVING OUR SECOND TKOF CLRNC THINGS SEEMS TO BE WORKING. WE TOOK OFF AND JUST AFTER TKOF EVERYTHING FAILED AGAIN AND DIDN'T COME BACK IN FLT. BY THIS TIME WE WERE 10-20 MI AWAY FROM THE ARPT WHEN WE DECIDED TO RETURN TO LGA. THE CAPT OPTED TO RETURN TO THIS ARPT BECAUSE THIS IS WHERE WE PICKED UP OUR PAX AND BECAUSE THIS WAS THE ARPT WE HAD JUST LEFT. I HAD STRONGLY SUGGESTED THAT WE GO TO A DIFFERENT ARPT; SUCH AS TETERBORO ARPT; OR SOME OTHER ARPT THAT WAS NOT AS BUSY. THIS SUGGESTION WAS LISTENED TO BUT THAT'S IT. WE HAD BEEN SWITCHED TO A COUPLE OF DIFFERENT CTLRS WHO WERE GIVING US NO GYRO VECTORS TO HELP US TRY AND FIND THE ARPT. AT THIS TIME WE HAD NO REF TO HDG AND NO NAV CAPABILITY. WE WERE GIVEN THESE HDG BACK TO LGA. AT ONE POINT WE THOUGHT WE HAD THE ARPT IN SIGHT SO THE CTLR SWITCHED US TO THE TWR CTLR AT LGA. EITHER DURING THE TURNING AND OR DURING ALL THE CONFUSION WE LOST SIGHT OF THE ARPT AND THE TWR CTLR TOLD US TO GO BACK TO THE APCH CTLR FOR VECTORS. UPON RETURNING TO THE APCH CTLR'S FREQ HE GAVE US HDG TO FLY AND FIXES TO FLY TO HELP US GET ESTABLISHED ON ANOTHER VISUAL APCH FOR THE ARPT. AT ONE POINT DURING ALL OF THIS THE CAPT LOST A COUPLE HUNDRED FEET ON HIS ALT AND ATC REMINDED US TO HOLD 3000 FT. ONCE WE FINALLY GOT THE ARPT IN SIGHT AGAIN WE LANDED WITHOUT INCIDENT AND TAXIED BACK TO THE FBO WHERE WE TRIED TROUBLESHOOTING THE PROB. AFTER A FEW HRS OF TROUBLESHOOTING AND THEN SHUTTING THE AIRPLANE DOWN WE WENT BACK TO AIRPLANE TO SEE IF IT HAD FIXED ITSELF; EVERYTHING SEEMED TO BE WORKING FINE. WE STARTED IT BACK UP AND TAXIED BACK OUT FOR TKOF; AFTER ANOTHER HALF HR TAXI; AND TOOK OFF FOR BRADLEY WINDSOR LOCKS; CT (BDL) FOR MAINT; JUST TO BE SURE EVERYTHING WAS FINE. EVERYTHING SEEMED TO BE WORKING ON THAT FLT AND WE LANDED SAFELY AT BDL. THE HDG INFO SEEMED TO BE OFF AT TIMES BUT NEVER MORE THAN 5-6 DEGS. IT WAS HARD TO TELL; WE BOTH HAD SOME DOUBT FROM THE EARLIER EVENTS. AS FOR HOW THIS COULD HAVE BEEN FIXED OR DONE BETTER? I STILL THINK WE SHOULD HAVE GONE TO ANOTHER ARPT OTHER THAN LGA. ALSO; LEARNING FROM THE DIFFERENT LITTLE THINGS GOING ON IN THE AIRPLANE TELLING YOU THAT SOMETHING IS WRONG; LIKE THE STORM-SCOPE; IS A GOOD THING. COME TO FIND OUT THE STORM-SCOPE NEEDS HDG REF INFO TO WORK; NEITHER ONE OF US KNEW THAT BEFORE THIS EVENT. I DON'T THINK WE DID ANYTHING WRONG OR VIOLATED ANY RULE BUT WE CERTAINLY CAUSED A GOOD AMOUNT OF CONFUSION AND I'M SURE FRUSTRATION. WHILE I'M SURE ALL OF THIS WAS GOOD PRACTICE FOR THE AIR TFC CTLRS OF NEW YORK; THEY PROBABLY DIDN'T NEED ANY MORE CONFUSION THAN WHAT THEY ALREADY HAD ON A NORMAL DAY. I KNOW THEY ARE EXTREMELY BUSY AND HAVE A HUGE RESPONSIBILITY. I AGAIN THANK THEM FOR THEIR HELP ON THAT DAY AND EVERY OTHER DAY THAT I FLY INTO THEIR AIRSPACE. THEY DO A GREAT JOB; ONE THAT I COULD NEVER DO. THIS WAS A GOOD LEARNING EXPERIENCE AND I HOPE IT NEVER HAPPENS AGAIN.